All signs point to an announcement next week of President Barack Obama’s Supreme Court pick, as Senators emerged from a White House meeting with the president on Wednesday suggesting a choice could come within days.

Several names are getting extensive play, but the cloak of secrecy draped over the selection process means only a few know for sure who will be selected and a surprise is certainly possible.

A choice has probably been in the pipeline for some time, as Obama aides have been preparing for the possibility of a pick since the transition.

In addition, Senate Judiciary Chairman Patrick Leahy (D-Vt.) has suggested he knew about Supreme Court Justice David Souter’s planned departure for some time before Souter announced it, and it is unlikely that he wouldn’t have alerted the White House — or that Souter himself would tell Leahy but not the president.

If Obama chooses Solicitor General Elena Kagan — who is among a handful of leading candidates mentioned by observers — he presumably would be ready to move anytime. Kagan has already been vetted by the Obama team, which combed her record before the president tapped her for her current position.

Several members of Obama’s staff, including Chief of Staff Rahm Emanuel, worked directly with Kagan when she was a White House domestic policy adviser under former President Bill Clinton. She is also well known to Obama himself, who was a colleague when both taught law at the University of Chicago.

Obama and his advisers know her ideology and know she wouldn’t wander toward the conservative wing once on the court. She also is well-respected by Senators. Among the lawmakers who have worked closely with Kagan is Sen. John McCain (R-Ariz.), Obama’s defeated rival for the presidency. Kagan was a key White House point person on the tobacco bill McCain crafted in 1998, and she logged long hours with him and his staff pushing the bill through the Commerce Committee, which he then chaired. The bill failed on the Senate floor.

Among her other strengths is what Obama aides view as a sharp mind that can engage with the likes of conservative heavyweights such as Chief Justice John Roberts and Justice Antonin Scalia. But Kagan has never been a judge, had never argued before the Supreme Court prior to her appointment as solicitor general, and has little track record on the great legal issues of the day.

Two other names float repeatedly to the top of the likely candidate lists, though neither has the same cachet with Obama and his aides. One intriguing possibility is Sonia Sotomayor, a federal appeals court judge who would be the first Hispanic on the court and would add another woman to the roster.

Sotomayor, whose father was Puerto Rican, has years of experience as a judge and was originally nominated for a federal district court judgeship by former President George H.W. Bush in 1992. She was appointed to her current position in 1998 by former President Bill Clinton.

It is possible that when Obama talks about picking a justice with a capacity for “empathy,— he is thinking about Sotomayor. Her father died when she was only nine and she rose out of a hardscrabble existence in the South Bronx.

But some analysts politely suggest that Sotomayor would not be the first choice of a president looking to add substantial intellectual heft to the left wing of the court. And she is also said to be prickly and sometimes tough to get along with — though this may matter less to a president who made Emanuel his chief of staff. In addition, Obama aides expect to be able to make more picks, and it may work better politically to nominate a Hispanic a little closer to Election Day 2012.

Another veteran judge at the top of the list of potential candidates is Diane Wood, a federal appeals court judge. She is known as a careful jurist who is widely respected for her intellectual heft.

The first black president may also have some inclination to pick a black jurist. For sure, an African-American already sits on the court, but not one who is ideologically aligned with Obama or many other Democrats. In that case, Obama may be looking at Leah Ward Sears, who is chief justice of the Georgia Supreme Court. Sears, who would be the first female African-American Supreme Court justice, is already a trailblazer, having been the first woman and youngest person to serve on the Georgia Supreme Court.

There is also talk that Obama may choose an openly homosexual justice. Some of his backers in the gay community are said to be unhappy that he did not place an openly gay person in his Cabinet.